Everything Richard wrote is correct. He only forgot to say that that
all these statements are true as statements about *complex numbers*.
Thus instead of saying "x/0 is undefined ..." he should have said "is
undefined as a complex number" or "is not a complex number" etc. The
word "number" is ambiguous, and there are some strange people, even
some mathematicians, who call things like Infinity "numbers" but I have
never heard of anyone refer to them as "complex numbers'. ("Complex" of
course includes "real").
(Besides, I don't believe that there is anyone, including yourself, who
really did not understand what Richard meant.)
Andrzej Kozlowski
Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/http://www.mimuw.edu.pl/~akoz/
On 2 Nov 2004, at 16:05, David W. Cantrell wrote:
>
> rwprogrammer at hotmail.com (Richard) wrote:
> [snip]
>> Mathematica handles 0 appropriately. x/0 is undefined for any number
>> x.
>
> In Mathematica, it is _not_ true that "x/0 is undefined for any number
> x."
> Rather, for any nonzero x, x/0 is defined as ComplexInfinity.
>
>> This is extremely simple to see if only you view division as the
>> opposite of multipication.
>
> That view of division is simply inadequate in number systems (such as
> the
> extended complex numbers) in which division of nonzero quantities by
> zero
> is defined.
>
>> A/B = C implies that C * B = A.
>>
>> 12/4 = 3 because 3*4 = 12.
>> 0/7 = 0 because 0*7 = 0.
>> 7/0 is undefined because x*0 does not equal 7 for any number x.
>> Therefore it has no answer (except undefined).
>
> In Mathematica, 7/0 yields ComplexInfinity, but that certainly does not
> imply that 0 * ComplexInfinity = 7. (In fact, 0 * ComplexInfinity is
> Indeterminate in Mathematica.)
>
> David Cantrell
>
>